This isn't something that can be done via an app. ConnectIQ doesn't allow access to the underlying file system, so an app would have no way to get the fit file to send.
That said, you don't need to connect a cable to your device at all. Assuming you've configured your device to automatically upload your data to Garmin Connect, you should just need to go to the activity page on Garmin Connect, click the gear icon in the top right corner, then pick Export Original and download the original fit file.
